### (math-poly-base-top-expr): New variable.

```(math-polynomial-p1): Replace variable mpb-top-expr by declared
variable.
(math-poly-base-total-base): New variable.
(math-total-polynomial-base, math-polynomial-p1): Replace variable
mpb-total-base by declared variable.
(math-factored-vars, math-to-list): Declare it.
(math-fact-expr): New variable.
(calcFunc-factors, calcFunc-factor, math-factor-expr,
math-factor-expr-try, math-factor-expr-part): Replace variable expr by
declared variable.
(math-fet-x): New variable.
(math-factor-expr-try, math-factor-poly-coefs): Replace variable x by
declared variable.
(math-factor-poly-coefs): Make temp a local variable.```
parent 885e6671
 ... ... @@ -516,48 +516,72 @@ ;;; Given an expression find all variables that are polynomial bases. ;;; Return list in the form '( (var1 degree1) (var2 degree2) ... ). ;;; Note dynamic scope of mpb-total-base. ;; The variable math-poly-base-total-base is local to ;; math-total-polynomial-base, but is used by math-polynomial-p1, ;; which is called by math-total-polynomial-base. (defvar math-poly-base-total-base) (defun math-total-polynomial-base (expr) (let ((mpb-total-base nil)) (let ((math-poly-base-total-base nil)) (math-polynomial-base expr 'math-polynomial-p1) (math-sort-poly-base-list mpb-total-base))) (math-sort-poly-base-list math-poly-base-total-base))) ;; The variable math-poly-base-top-expr is local to math-polynomial-base ;; in calc-alg.el, but is used by math-polynomial-p1 which is called ;; by math-polynomial-base. (defvar math-poly-base-top-expr) (defun math-polynomial-p1 (subexpr) (or (assoc subexpr mpb-total-base) (or (assoc subexpr math-poly-base-total-base) (memq (car subexpr) '(+ - * / neg)) (and (eq (car subexpr) '^) (natnump (nth 2 subexpr))) (let* ((math-poly-base-variable subexpr) (exponent (math-polynomial-p mpb-top-expr subexpr))) (exponent (math-polynomial-p math-poly-base-top-expr subexpr))) (if exponent (setq mpb-total-base (cons (list subexpr exponent) mpb-total-base))))) (setq math-poly-base-total-base (cons (list subexpr exponent) math-poly-base-total-base))))) nil) ;; The variable math-factored-vars is local to calcFunc-factors and ;; calcFunc-factor, but is used by math-factor-expr and ;; math-factor-expr-part, which are called (directly and indirectly) by ;; calcFunc-factor and calcFunc-factors. (defvar math-factored-vars) ;; The variable math-fact-expr is local to calcFunc-factors, ;; calcFunc-factor and math-factor-expr, but is used by math-factor-expr-try ;; and math-factor-expr-part, which are called (directly and indirectly) by ;; calcFunc-factor, calcFunc-factors and math-factor-expr. (defvar math-fact-expr) ;; The variable math-to-list is local to calcFunc-factors and ;; calcFunc-factor, but is used by math-accum-factors, which is ;; called (indirectly) by calcFunc-factors and calcFunc-factor. (defvar math-to-list) (defun calcFunc-factors (expr &optional var) (defun calcFunc-factors (math-fact-expr &optional var) (let ((math-factored-vars (if var t nil)) (math-to-list t) (calc-prefer-frac t)) (or var (setq var (math-polynomial-base expr))) (setq var (math-polynomial-base math-fact-expr))) (let ((res (math-factor-finish (or (catch 'factor (math-factor-expr-try var)) expr)))) math-fact-expr)))) (math-simplify (if (math-vectorp res) res (list 'vec (list 'vec res 1))))))) (defun calcFunc-factor (expr &optional var) (defun calcFunc-factor (math-fact-expr &optional var) (let ((math-factored-vars nil) (math-to-list nil) (calc-prefer-frac t)) (math-simplify (math-factor-finish (if var (let ((math-factored-vars t)) (or (catch 'factor (math-factor-expr-try var)) expr)) (math-factor-expr expr)))))) (or (catch 'factor (math-factor-expr-try var)) math-fact-expr)) (math-factor-expr math-fact-expr)))))) (defun math-factor-finish (x) (if (Math-primp x) ... ... @@ -571,18 +595,18 @@ (list 'calcFunc-Fac-Prot x) x)) (defun math-factor-expr (expr) (cond ((eq math-factored-vars t) expr) ((or (memq (car-safe expr) '(* / ^ neg)) (assq (car-safe expr) calc-tweak-eqn-table)) (cons (car expr) (mapcar 'math-factor-expr (cdr expr)))) ((memq (car-safe expr) '(+ -)) (defun math-factor-expr (math-fact-expr) (cond ((eq math-factored-vars t) math-fact-expr) ((or (memq (car-safe math-fact-expr) '(* / ^ neg)) (assq (car-safe math-fact-expr) calc-tweak-eqn-table)) (cons (car math-fact-expr) (mapcar 'math-factor-expr (cdr math-fact-expr)))) ((memq (car-safe math-fact-expr) '(+ -)) (let* ((math-factored-vars math-factored-vars) (y (catch 'factor (math-factor-expr-part expr)))) (y (catch 'factor (math-factor-expr-part math-fact-expr)))) (if y (math-factor-expr y) expr))) (t expr))) math-fact-expr))) (t math-fact-expr))) (defun math-factor-expr-part (x) ; uses "expr" (if (memq (car-safe x) '(+ - * / ^ neg)) ... ... @@ -590,21 +614,25 @@ (math-factor-expr-part (car x))) (and (not (Math-objvecp x)) (not (assoc x math-factored-vars)) (> (math-factor-contains expr x) 1) (> (math-factor-contains math-fact-expr x) 1) (setq math-factored-vars (cons (list x) math-factored-vars)) (math-factor-expr-try x)))) (defun math-factor-expr-try (x) (if (eq (car-safe expr) '*) (let ((res1 (catch 'factor (let ((expr (nth 1 expr))) (math-factor-expr-try x)))) (res2 (catch 'factor (let ((expr (nth 2 expr))) (math-factor-expr-try x))))) ;; The variable math-fet-x is local to math-factor-expr-try, but is ;; used by math-factor-poly-coefs, which is called by math-factor-expr-try. (defvar math-fet-x) (defun math-factor-expr-try (math-fet-x) (if (eq (car-safe math-fact-expr) '*) (let ((res1 (catch 'factor (let ((math-fact-expr (nth 1 math-fact-expr))) (math-factor-expr-try math-fet-x)))) (res2 (catch 'factor (let ((math-fact-expr (nth 2 math-fact-expr))) (math-factor-expr-try math-fet-x))))) (and (or res1 res2) (throw 'factor (math-accum-factors (or res1 (nth 1 expr)) 1 (or res2 (nth 2 expr)))))) (let* ((p (math-is-polynomial expr x 30 'gen)) (math-poly-modulus (math-poly-modulus expr)) (throw 'factor (math-accum-factors (or res1 (nth 1 math-fact-expr)) 1 (or res2 (nth 2 math-fact-expr)))))) (let* ((p (math-is-polynomial math-fact-expr math-fet-x 30 'gen)) (math-poly-modulus (math-poly-modulus math-fact-expr)) res) (and (cdr p) (setq res (math-factor-poly-coefs p)) ... ... @@ -642,11 +670,11 @@ (math-mul (math-pow fac pow) facs))) (defun math-factor-poly-coefs (p &optional square-free) ; uses "x" (let (t1 t2) (let (t1 t2 temp) (cond ((not (cdr p)) (or (car p) 0)) ;; Strip off multiples of x. ;; Strip off multiples of math-fet-x. ((Math-zerop (car p)) (let ((z 0)) (while (and p (Math-zerop (car p))) ... ... @@ -654,7 +682,7 @@ (if (cdr p) (setq p (math-factor-poly-coefs p square-free)) (setq p (math-sort-terms (math-factor-expr (car p))))) (math-accum-factors x z (math-factor-protect p)))) (math-accum-factors math-fet-x z (math-factor-protect p)))) ;; Factor out content. ((and (not square-free) ... ... @@ -665,12 +693,12 @@ (math-accum-factors t1 1 (math-factor-poly-coefs (math-poly-div-list p t1) 'cont))) ;; Check if linear in x. ;; Check if linear in math-fet-x. ((not (cdr (cdr p))) (math-add (math-factor-protect (math-sort-terms (math-factor-expr (car p)))) (math-mul x (math-factor-protect (math-mul math-fet-x (math-factor-protect (math-sort-terms (math-factor-expr (nth 1 p))))))) ... ... @@ -683,7 +711,7 @@ (setq pp (cdr pp))) pp) (let ((res (math-rewrite (list 'calcFunc-thecoefs x (cons 'vec p)) (list 'calcFunc-thecoefs math-fet-x (cons 'vec p)) '(var FactorRules var-FactorRules)))) (or (and (eq (car-safe res) 'calcFunc-thefactors) (= (length res) 3) ... ... @@ -693,7 +721,7 @@ (while (setq vec (cdr vec)) (setq facs (math-accum-factors (car vec) 1 facs))) facs)) (math-build-polynomial-expr p x)))) (math-build-polynomial-expr p math-fet-x)))) ;; Check if rational coefficients (i.e., not modulo a prime). ((eq math-poly-modulus 1) ... ... @@ -724,12 +752,13 @@ (setq scale (math-div scale den)) (math-add (math-add (math-mul den (math-pow x 2)) (math-mul (math-mul coef1 den) x)) (math-mul den (math-pow math-fet-x 2)) (math-mul (math-mul coef1 den) math-fet-x)) (math-mul coef0 den))) (let ((den (math-lcm-denoms coef0))) (setq scale (math-div scale den)) (math-add (math-mul den x) (math-add (math-mul den math-fet-x) (math-mul coef0 den)))) 1 expr) roots (cdr roots)))) ... ... @@ -738,8 +767,8 @@ (math-mul csign (math-build-polynomial-expr (math-mul-list (nth 1 t1) scale) x))))) (math-build-polynomial-expr p x)) ; can't factor it. math-fet-x))))) (math-build-polynomial-expr p math-fet-x)) ; can't factor it. ;; Separate out the squared terms (Knuth exercise 4.6.2-34). ;; This step also divides out the content of the polynomial. ... ...
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